internal void Copy( ChineseRemainder ToCopy )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
DigitsArray[Count] = ToCopy.DigitsArray[Count];
}
}
internal CRTBaseMath( BackgroundWorker UseWorker, CRTMath UseCRTMath )
{
// Most of these are created ahead of time so that
// they don't have to be created inside a loop.
Worker = UseWorker;
IntMath = new IntegerMath();
CRTMath1 = UseCRTMath;
Quotient = new Integer();
Remainder = new Integer();
CRTAccumulateBase = new ChineseRemainder( IntMath );
CRTAccumulateBasePart = new ChineseRemainder( IntMath );
CRTAccumulateForBaseMultiples = new ChineseRemainder( IntMath );
CRTAccumulatePart = new ChineseRemainder( IntMath );
BaseModArrayModulus = new Integer();
CRTTempForIsEqual = new ChineseRemainder( IntMath );
CRTWorkingTemp = new ChineseRemainder( IntMath );
ExponentCopy = new Integer();
CRTXForModPower = new ChineseRemainder( IntMath );
CRTAccumulate = new ChineseRemainder( IntMath );
CRTCopyForSquare = new ChineseRemainder( IntMath );
FermatExponent = new Integer();
CRTFermatModulus = new ChineseRemainder( IntMath );
FermatModulus = new Integer();
CRTTestFermat = new ChineseRemainder( IntMath );
Worker.ReportProgress( 0, "Setting up numbers array." );
SetupNumbersArray();
Worker.ReportProgress( 0, "Setting up base array." );
SetupBaseArray();
Worker.ReportProgress( 0, "Setting up multiplicative inverses." );
SetMultiplicativeInverses();
}
internal void Add( ChineseRemainder ToAdd )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
// Operations like this could be very fast if they were done in
// hardware, and the small mod operations could be done in very
// small hardware lookup tables. They could also be done in parallel,
// which would make it a lot faster than the way this is done, one
// digit at a time. Notice that there is no carry operation here.
// As Claud Shannon would say, there is no diffusion here.
// Like he wrote about in A Mathematical Theory of Cryptography.
DigitsArray[Count].Value += ToAdd.DigitsArray[Count].Value;
if( DigitsArray[Count].Value >= DigitsArray[Count].Prime )
DigitsArray[Count].Value -= DigitsArray[Count].Prime;
// DigitsArray[Count].Value = DigitsArray[Count].Value % DigitsArray[Count].Prime;
}
}
internal void Add( ChineseRemainder ToAdd )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
// Operations like this could be very fast if
// they were done in hardware, and the small
// mod operations could be done in very small
// hardware lookup tables. They could also be
// done in parallel, which would make it a lot
// faster than the way this is done, one digit
// at a time. Notice that there is no carry
// operation here. As Claud Shannon would say,
// there is no diffusion here.
DigitsArray[Count] += ToAdd.DigitsArray[Count];
int Prime = (int)IntMath.GetPrimeAt( Count );
if( DigitsArray[Count] >= Prime )
DigitsArray[Count] -= Prime;
// DigitsArray[Count] = DigitsArray[Count] % Prime;
}
}
internal bool IsEqual( ChineseRemainder ToCheck )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
if( DigitsArray[Count].Value != ToCheck.DigitsArray[Count].Value )
return false;
}
return true;
}
private void SetupNumbersArray()
{
try
{
uint BiggestPrime = IntMath.GetPrimeAt( CRTBase.DigitsArraySize + 1 );
NumbersArray = new ChineseRemainder[BiggestPrime];
Integer SetNumber = new Integer();
for( uint Count = 0; Count < BiggestPrime; Count++ )
{
SetNumber.SetFromULong( Count );
ChineseRemainder CRTSetNumber = new ChineseRemainder( IntMath );
CRTSetNumber.SetFromTraditionalInteger( SetNumber );
NumbersArray[Count] = CRTSetNumber;
}
}
catch( Exception Except )
{
throw( new Exception( "Exception in SetupNumbersArray(): " + Except.Message ));
}
}
// These bottom digits are 0 for each prime that gets
// multiplied by the base. So they keep getting one
// more zero at the bottom of each one.
// But the digits in BaseModArray only have the zeros
// at the bottom on the ones that are smaller than the
// modulus.
// At BaseArray[0] it's 1, 1, 1, 1, 1, .... for all of them.
// 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0
// 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 0, 0
// 30, 30, 30, 30, 1, 7, 11, 13, 4, 8, 2, 0, 0, 0
private void SetupBaseArray()
{
// The first few numbers for the base:
// 2 2
// 3 6
// 5 30
// 7 210
// 11 2,310
// 13 30,030
// 17 510,510
// 19 9,699,690
// 23 223,092,870
try
{
if( NumbersArray == null )
throw( new Exception( "NumbersArray should have already been setup in SetupBaseArray()." ));
BaseStringsArray = new string[ChineseRemainder.DigitsArraySize];
BaseArray = new Integer[ChineseRemainder.DigitsArraySize];
CRTBaseArray = new ChineseRemainder[ChineseRemainder.DigitsArraySize];
Integer SetBase = new Integer();
ChineseRemainder CRTSetBase = new ChineseRemainder( IntMath );
Integer BigBase = new Integer();
ChineseRemainder CRTBigBase = new ChineseRemainder( IntMath );
BigBase.SetFromULong( 2 );
CRTBigBase.SetFromUInt( 2 );
string BaseS = "2";
SetBase.SetToOne();
CRTSetBase.SetToOne();
// The base at zero is 1.
BaseArray[0] = SetBase;
CRTBaseArray[0] = CRTSetBase;
BaseStringsArray[0] = "1";
ChineseRemainder CRTTemp = new ChineseRemainder( IntMath );
// The first time through the loop the base
// is set to 2.
// So BaseArray[0] = 1;
// So BaseArray[1] = 2;
// So BaseArray[2] = 6;
// So BaseArray[3] = 30;
// And so on...
// In BaseArray[3] digits at 2, 3 and 5 are set to zero.
// In BaseArray[4] digits at 2, 3, 5 and 7 are set to zero.
for( int Count = 1; Count < ChineseRemainder.DigitsArraySize; Count++ )
{
SetBase = new Integer();
CRTSetBase = new ChineseRemainder( IntMath );
SetBase.Copy( BigBase );
CRTSetBase.Copy( CRTBigBase );
BaseStringsArray[Count] = BaseS;
BaseArray[Count] = SetBase;
CRTBaseArray[Count] = CRTSetBase;
// if( Count < 50 )
// Worker.ReportProgress( 0, CRTBaseArray[Count].GetString() );
if( !IsEqualToInteger( CRTBaseArray[Count],
BaseArray[Count] ))
throw( new Exception( "Bug. The bases aren't equal." ));
// Multiply it for the next BigBase.
uint Prime = IntMath.GetPrimeAt( Count );
BaseS = BaseS + "*" + Prime.ToString();
IntMath.MultiplyUInt( BigBase, Prime );
CRTBigBase.Multiply( NumbersArray[IntMath.GetPrimeAt( Count )] );
}
}
catch( Exception Except )
{
throw( new Exception( "Exception in SetupBaseArray(): " + Except.Message ));
}
}
// CRTBaseModArray doesn't have the pattern of zeros
// down to the end like in CRTBaseArray.
internal void SetupBaseModArray( Integer Modulus )
{
try
{
BaseModArrayModulus = Modulus;
if( NumbersArray == null )
throw( new Exception( "NumbersArray should have already been setup in SetupBaseModArray()." ));
CRTBaseModArray = new ChineseRemainder[ChineseRemainder.DigitsArraySize];
ChineseRemainder CRTSetBase = new ChineseRemainder( IntMath );
Integer BigBase = new Integer();
ChineseRemainder CRTBigBase = new ChineseRemainder( IntMath );
BigBase.SetFromULong( 2 );
CRTBigBase.SetFromUInt( 2 );
CRTSetBase.SetToOne();
CRTBaseModArray[0] = CRTSetBase;
ChineseRemainder CRTTemp = new ChineseRemainder( IntMath );
for( int Count = 1; Count < ChineseRemainder.DigitsArraySize; Count++ )
{
CRTSetBase = new ChineseRemainder( IntMath );
CRTSetBase.Copy( CRTBigBase );
CRTBaseModArray[Count] = CRTSetBase;
// Multiply it for the next BigBase.
IntMath.MultiplyUInt( BigBase, IntMath.GetPrimeAt( Count ));
IntMath.Divide( BigBase, Modulus, Quotient, Remainder );
BigBase.Copy( Remainder );
CRTBigBase.SetFromTraditionalInteger( BigBase );
}
}
catch( Exception Except )
{
throw( new Exception( "Exception in SetupBaseModArray(): " + Except.Message ));
}
}
// Copyright Eric Chauvin.
internal void Multiply( ChineseRemainder ToMul )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
// There is no Diffusion here either, like the
// kind that Claude Shannon wrote about in
// A Mathematical Theory of Cryptography.
DigitsArray[Count] *= ToMul.DigitsArray[Count];
DigitsArray[Count] %= (int)IntMath.GetPrimeAt( Count );
}
}
internal void Subtract( ChineseRemainder ToSub )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
DigitsArray[Count].Value -= ToSub.DigitsArray[Count].Value;
if( DigitsArray[Count].Value < 0 )
DigitsArray[Count].Value += DigitsArray[Count].Prime;
}
}
internal void ModularPower( ChineseRemainder CRTResult,
Integer Exponent,
ChineseRemainder CRTModulus,
bool UsePresetBaseArray )
{
// The square and multiply method is in Wikipedia:
// https://en.wikipedia.org/wiki/Exponentiation_by_squaring
if( Worker.CancellationPending )
return;
if( CRTResult.IsZero())
return; // With CRTResult still zero.
if( CRTResult.IsEqual( CRTModulus ))
{
// It is congruent to zero % ModN.
CRTResult.SetToZero();
return;
}
// Result is not zero at this point.
if( Exponent.IsZero() )
{
CRTResult.SetToOne();
return;
}
Integer Result = new Integer();
CRTMath1.GetTraditionalInteger( Result, CRTResult );
Integer Modulus = new Integer();
CRTMath1.GetTraditionalInteger( Modulus, CRTModulus );
if( Modulus.ParamIsGreater( Result ))
{
// throw( new Exception( "This is not supposed to be input for RSA plain text." ));
IntMath.Divide( Result, Modulus, Quotient, Remainder );
Result.Copy( Remainder );
CRTResult.SetFromTraditionalInteger( Remainder );
}
if( Exponent.IsEqualToULong( 1 ))
{
// Result stays the same.
return;
}
if( !UsePresetBaseArray )
SetupBaseModArray( Modulus );
if( CRTBaseModArray == null )
throw( new Exception( "SetupBaseModArray() should have already been done here." ));
CRTXForModPower.Copy( CRTResult );
ExponentCopy.Copy( Exponent );
int TestIndex = 0;
CRTResult.SetToOne();
int LoopsTest = 0;
while( true )
{
LoopsTest++;
if( (ExponentCopy.GetD( 0 ) & 1) == 1 ) // If the bottom bit is 1.
{
CRTResult.Multiply( CRTXForModPower );
ModularReduction( CRTResult, CRTAccumulate );
CRTResult.Copy( CRTAccumulate );
}
ExponentCopy.ShiftRight( 1 ); // Divide by 2.
if( ExponentCopy.IsZero())
break;
// Square it.
CRTCopyForSquare.Copy( CRTXForModPower );
CRTXForModPower.Multiply( CRTCopyForSquare );
ModularReduction( CRTXForModPower, CRTAccumulate );
CRTXForModPower.Copy( CRTAccumulate );
}
ModularReduction( CRTResult, CRTAccumulate );
CRTResult.Copy( CRTAccumulate );
// Division is never used in the loop above.
// This is a very small Quotient.
// See SetupBaseMultiples() for a description of how to calculate
// the maximum size of this quotient.
CRTMath1.GetTraditionalInteger( Result, CRTResult );
IntMath.Divide( Result, Modulus, Quotient, Remainder );
// Is the Quotient bigger than a 32 bit integer?
if( Quotient.GetIndex() > 0 )
throw( new Exception( "I haven't ever seen this happen. Quotient.GetIndex() > 0. It is: " + Quotient.GetIndex().ToString() ));
QuotientForTest = Quotient.GetAsULong();
if( QuotientForTest > 2097867 )
throw( new Exception( "This can never happen unless I increase ChineseRemainder.DigitsArraySize." ));
Result.Copy( Remainder );
CRTResult.SetFromTraditionalInteger( Remainder );
}
// http://en.wikipedia.org/wiki/Primality_test
// http://en.wikipedia.org/wiki/Fermat_primality_test
internal bool IsFermatPrimeForOneValue( ChineseRemainder CRTToTest, uint Base )
{
// http://en.wikipedia.org/wiki/Carmichael_number
// Assume ToTest is not a small number. (Not the size of a small prime.)
// Normally it would be something like a 1024 bit number or bigger,
// but I assume it's at least bigger than a 32 bit number.
// Assume this has already been checked to see if it's divisible
// by a small prime.
// A has to be coprime to P and it is here because ToTest is not
// divisible by a small prime.
// Fermat's little theorem:
// A ^ (P - 1) is congruent to 1 mod P if P is a prime.
// Or: A^P - A is congrunt to A mod P.
// If you multiply A by itself P times then divide it by P,
// the remainder is A. (A^P / P)
// 5^3 = 125. 125 - 5 = 120. A multiple of 5.
// 2^7 = 128. 128 - 2 = 7 * 18 (a multiple of 7.)
CRTMath1.GetTraditionalInteger( FermatExponent, CRTToTest );
IntMath.SubtractULong( FermatExponent, 1 );
// This is a very small Modulus since it's being set from a uint.
CRTTestFermat.SetFromUInt( Base );
CRTFermatModulus.Copy( CRTToTest );
CRTMath1.GetTraditionalInteger( FermatModulus, CRTFermatModulus );
ModularPower( CRTTestFermat, FermatExponent, CRTFermatModulus, false );
if( CRTTestFermat.IsOne())
return true; // It passed the test. It _might_ be a prime.
else
return false; // It is _definitely_ a composite number.
}
internal bool IsFermatPrime( ChineseRemainder CRTToTest, int HowMany )
{
// Also see Rabin-Miller test.
// Also see Solovay-Strassen test.
// This Fermat primality test is usually described
// as using random primes to test with, and you
// could do it that way too.
// IntegerMath.PrimeArrayLength = 1024 * 32;
int StartAt = 1024 * 16; // Or much bigger.
for( int Count = StartAt; Count < (HowMany + StartAt); Count++ )
{
if( !IsFermatPrimeForOneValue( CRTToTest, IntMath.GetPrimeAt( Count )))
return false;
}
// It _might_ be a prime if it passed this test.
// Increasing HowMany increases the probability that it's a prime.
return true;
}
internal bool IsEqualToInteger( ChineseRemainder CRTTest, Integer Test )
{
CRTTempForIsEqual.SetFromTraditionalInteger( Test );
if( CRTTest.IsEqual( CRTTempForIsEqual ))
return true;
else
return false;
}
internal void Subtract( ChineseRemainder ToSub )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
DigitsArray[Count] -= ToSub.DigitsArray[Count];
if( DigitsArray[Count] < 0 )
DigitsArray[Count] += (int)IntMath.GetPrimeAt( Count );
}
}
// This is the closest this has to Divide().
internal void ModularInverse( ChineseRemainder ToDivide )
{
// ToDivide times what equals this number?
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
for( int CountPrime = 0; CountPrime < DigitsArray[Count].Prime; CountPrime++ )
{
int Test = CountPrime * ToDivide.DigitsArray[Count].Value;
Test = Test % DigitsArray[Count].Prime;
if( Test == DigitsArray[Count].Value )
{
DigitsArray[Count].Value = CountPrime;
break;
}
}
}
}
internal void Multiply( ChineseRemainder ToMul )
{
for( int Count = 0; Count < DigitsArraySize; Count++ )
{
// There is no Diffusion here either, like the kind that
// Claude Shannon wrote about in A Mathematical Theory of
// Cryptography.
DigitsArray[Count].Value *= ToMul.DigitsArray[Count].Value;
DigitsArray[Count].Value %= DigitsArray[Count].Prime;
}
}
// Copyright Eric Chauvin.
internal void ModularReduction( ChineseRemainder CRTInput,
ChineseRemainder CRTAccumulate )
{
try
{
if( NumbersArray == null )
throw( new Exception( "Bug: The NumbersArray should have been set up already." ));
if( CRTBaseModArray == null )
throw( new Exception( "Bug: The BaseModArray should have been set up already." ));
// This first one has the prime 2 as its base so it's going to
// be set to either zero or one.
if( CRTInput.GetDigitAt( 0 ) == 1 )
{
CRTAccumulate.SetToOne();
}
else
{
CRTAccumulate.SetToZero();
}
CRTBase CRTBaseInput = new CRTBase( IntMath );
int HowManyToAdd = SetFromCRTNumber( CRTBaseInput, CRTInput );
// Integer Test = new Integer();
// ChineseRemainder CRTTest = new ChineseRemainder( IntMath );
// GetTraditionalInteger( CRTBaseInput, Test );
// CRTTest.SetFromTraditionalInteger( Test );
// if( !CRTTest.IsEqual( CRTInput ))
// throw( new Exception( "CRTTest for CRTInput isn't right." ));
// Count starts at 1, so it's the prime 3.
for( int Count = 1; Count <= HowManyToAdd; Count++ )
{
// BaseMultiple is a number that is not bigger
// than the prime at this point. (The prime at:
// IntMath.GetPrimeAt( Count ).)
uint BaseMultiple = (uint)CRTBaseInput.GetDigitAt( Count );
// It uses the CRTBaseModArray here:
CRTWorkingTemp.Copy( CRTBaseModArray[Count] );
CRTWorkingTemp.Multiply( NumbersArray[BaseMultiple] );
CRTAccumulate.Add( CRTWorkingTemp );
}
}
catch( Exception Except )
{
throw( new Exception( "Exception in ModularReduction(): " + Except.Message ));
}
}
internal int SetFromCRTNumber( CRTBase ToSet, ChineseRemainder SetFrom )
{
try
{
if( NumbersArray == null )
throw( new Exception( "Bug: The NumbersArray should have been set up already." ));
// ToSet.SetToZero();
// CRTBaseArray[0] is 1.
if( SetFrom.GetDigitAt( 0 ) == 1 )
{
ToSet.SetToOne(); // 1 times 1 for this base.
CRTAccumulateForBaseMultiples.SetToOne();
}
else
{
ToSet.SetToZero();
CRTAccumulateForBaseMultiples.SetToZero();
}
int HighestNonZeroDigit = 1;
// Count starts at 1, so it's at the prime 3.
for( int Count = 1; Count < ChineseRemainder.DigitsArraySize; Count++ )
{
int Prime = (int)IntMath.GetPrimeAt( Count );
int AccumulateDigit = CRTAccumulateForBaseMultiples.GetDigitAt( Count );
int CRTInputTestDigit = SetFrom.GetDigitAt( Count );
int BaseDigit = CRTBaseArray[Count].GetDigitAt( Count );
if( BaseDigit == 0 )
throw( new Exception( "This never happens. BaseDigit == 0." ));
int BaseMult = CRTInputTestDigit;
if( BaseMult < AccumulateDigit )
BaseMult += Prime;
BaseMult -= AccumulateDigit;
int Inverse = MultInverseArray[Count, BaseDigit];
BaseMult = (BaseMult * Inverse) % Prime;
ToSet.SetDigitAt( BaseMult, Count );
if( BaseMult != 0 )
HighestNonZeroDigit = Count;
// Notice that this is using CRTBaseArray and not
// CRTBaseModArray.
// This would be very fast in parallel hardware,
// but not in software that has to do each digit
// one at a time.
CRTAccumulatePart.Copy( CRTBaseArray[Count] );
CRTAccumulatePart.Multiply( NumbersArray[BaseMult] );
CRTAccumulateForBaseMultiples.Add( CRTAccumulatePart );
}
return HighestNonZeroDigit;
}
catch( Exception Except )
{
throw( new Exception( "Exception in SetFromCRTNumber(): " + Except.Message ));
}
}
private void DoCRTTest( Integer StartingNumber )
{
CRTMath CRTMath1 = new CRTMath( Worker );
ECTime CRTTestTime = new ECTime();
ChineseRemainder CRTTest = new ChineseRemainder( IntMath );
ChineseRemainder CRTTest2 = new ChineseRemainder( IntMath );
ChineseRemainder CRTAccumulate = new ChineseRemainder( IntMath );
ChineseRemainder CRTToTest = new ChineseRemainder( IntMath );
ChineseRemainder CRTTempEqual = new ChineseRemainder( IntMath );
ChineseRemainder CRTTestEqual = new ChineseRemainder( IntMath );
Integer BigBase = new Integer();
Integer ToTest = new Integer();
Integer Accumulate = new Integer();
Integer Test1 = new Integer();
Integer Test2 = new Integer();
CRTTest.SetFromTraditionalInteger( StartingNumber );
// If the digit array size isn't set right in relation to
// Integer.DigitArraySize then it can cause an error here.
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( StartingNumber ))
throw( new Exception( " !Accumulate.IsEqual( Result )." ));
CRTTestEqual.SetFromTraditionalInteger( Accumulate );
if( !CRTMath1.IsEqualToInteger( CRTTestEqual, Accumulate ))
throw( new Exception( "IsEqualToInteger() didn't work." ));
// Make sure it works with even numbers too.
Test1.Copy( StartingNumber );
Test1.SetD( 0, Test1.GetD( 0 ) & 0xFE );
CRTTest.SetFromTraditionalInteger( Test1 );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( Test1 ))
throw( new Exception( "For even numbers. !Accumulate.IsEqual( Test )." ));
////////////
// Make sure the size of this works with the Integer size because
// an overflow is hard to find.
CRTTestTime.SetToNow();
Test1.SetToMaxValueForCRT();
CRTTest.SetFromTraditionalInteger( Test1 );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( Test1 ))
throw( new Exception( "For the max value. !Accumulate.IsEqual( Test1 )." ));
// Worker.ReportProgress( 0, "CRT Max test seconds: " + CRTTestTime.GetSecondsToNow().ToString( "N1" ));
// Worker.ReportProgress( 0, "MaxValue: " + IntMath.ToString10( Accumulate ));
// Worker.ReportProgress( 0, "MaxValue.Index: " + Accumulate.GetIndex().ToString());
// Multiplicative Inverse test:
Integer TestDivideBy = new Integer();
Integer TestProduct = new Integer();
ChineseRemainder CRTTestDivideBy = new ChineseRemainder( IntMath );
ChineseRemainder CRTTestProduct = new ChineseRemainder( IntMath );
TestDivideBy.Copy( StartingNumber );
TestProduct.Copy( StartingNumber );
IntMath.Multiply( TestProduct, TestDivideBy );
CRTTestDivideBy.SetFromTraditionalInteger( TestDivideBy );
CRTTestProduct.SetFromTraditionalInteger( TestDivideBy );
CRTTestProduct.Multiply( CRTTestDivideBy );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTestProduct );
if( !Accumulate.IsEqual( TestProduct ))
throw( new Exception( "Multiply test was bad." ));
IntMath.Divide( TestProduct, TestDivideBy, Quotient, Remainder );
if( !Remainder.IsZero())
throw( new Exception( "This test won't work unless it divides it exactly." ));
ChineseRemainder CRTTestQuotient = new ChineseRemainder( IntMath );
CRTMath1.MultiplicativeInverse( CRTTestProduct, CRTTestDivideBy, CRTTestQuotient );
// Yes, multiplicative inverse is the same number
// as with regular division.
Integer TestQuotient = new Integer();
CRTMath1.GetTraditionalInteger( TestQuotient, CRTTestQuotient );
if( !TestQuotient.IsEqual( Quotient ))
throw( new Exception( "Modular Inverse in DoCRTTest didn't work." ));
// Subtract
Test1.Copy( StartingNumber );
IntMath.SetFromString( Test2, "12345678901234567890123456789012345" );
CRTTest.SetFromTraditionalInteger( Test1 );
CRTTest2.SetFromTraditionalInteger( Test2 );
CRTTest.Subtract( CRTTest2 );
IntMath.Subtract( Test1, Test2 );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( Test1 ))
throw( new Exception( "Subtract test was bad." ));
// Add
Test1.Copy( StartingNumber );
IntMath.SetFromString( Test2, "12345678901234567890123456789012345" );
CRTTest.SetFromTraditionalInteger( Test1 );
CRTTest2.SetFromTraditionalInteger( Test2 );
CRTTest.Add( CRTTest2 );
IntMath.Add( Test1, Test2 );
CRTMath1.GetTraditionalInteger( Accumulate, CRTTest );
if( !Accumulate.IsEqual( Test1 ))
throw( new Exception( "Add test was bad." ));
/////////
CRTBaseMath CBaseMath = new CRTBaseMath( Worker, CRTMath1 );
ChineseRemainder CRTInput = new ChineseRemainder( IntMath );
CRTInput.SetFromTraditionalInteger( StartingNumber );
Test1.Copy( StartingNumber );
IntMath.SetFromString( Test2, "12345678901234567890123456789012345" );
IntMath.Add( Test1, Test2 );
Integer TestModulus = new Integer();
TestModulus.Copy( Test1 );
ChineseRemainder CRTTestModulus = new ChineseRemainder( IntMath );
CRTTestModulus.SetFromTraditionalInteger( TestModulus );
Integer Exponent = new Integer();
Exponent.SetFromULong( PubKeyExponentUint );
CBaseMath.ModularPower( CRTInput, Exponent, CRTTestModulus, false );
IntMath.IntMathNew.ModularPower( StartingNumber, Exponent, TestModulus, false );
if( !CRTMath1.IsEqualToInteger( CRTInput, StartingNumber ))
throw( new Exception( "CRTBase ModularPower() didn't work." ));
CRTBase ExpTest = new CRTBase( IntMath );
CBaseMath.SetFromCRTNumber( ExpTest, CRTInput );
CBaseMath.GetExponentForm( ExpTest, 37 );
// Worker.ReportProgress( 0, "CRT was good." );
}